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The domain of f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction is

  1. R minus left curly bracket negative 1 , 2 right curly bracket    
  2. left parenthesis negative 2 comma infinity right parenthesis    
  3. R minus left curly bracket negative 1 comma negative 2 comma negative 3 right curly bracket    
  4. left parenthesis negative 3 comma infinity right parenthesis minus left curly bracket negative 1 comma negative 2 right curly bracket    

Hint:

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The correct answer is: left parenthesis negative 3 comma infinity right parenthesis minus left curly bracket negative 1 comma negative 2 right curly bracket


    f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction
    For f(x) to be defined :
    1) (x + 3) > 0
    rightwards double arrowx > -3
    2) x to the power of 2 space end exponent plus space 3 x space plus space 2 space space not equal to space 0
    B y space f a c t o r i z a t i o n space left parenthesis s p l i t t i n g space o f space m i d d l e space t e r m s right parenthesis
rightwards double arrow left parenthesis x space plus 1 right parenthesis left parenthesis x plus 2 right parenthesis space space not equal to space 0
rightwards double arrow x space space not equal to space left parenthesis negative 1 comma negative 2 right parenthesis
    Thus, Domain of f(x)  will be (-3, infinity) - (-1,-2)

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